What are the divisors of 2202?

1, 2, 3, 6, 367, 734, 1101, 2202

There is a total of 8 positive divisors.
The sum of these divisors is 4416.
The arithmetic mean is 552.

4 even divisors

2, 6, 734, 2202

4 odd divisors

1, 3, 367, 1101

How to compute the divisors of 2202?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2202 by each of the numbers from 1 to 2202 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2202 / 1 = 2202 (the remainder is 0, so 1 is a divisor of 2202)
2202 / 2 = 1101 (the remainder is 0, so 2 is a divisor of 2202)
2202 / 3 = 734 (the remainder is 0, so 3 is a divisor of 2202)
...
2202 / 2201 = 1.0004543389368 (the remainder is 1, so 2201 is not a divisor of 2202)
2202 / 2202 = 1 (the remainder is 0, so 2202 is a divisor of 2202)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2202 (i.e. 46.9254728266). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2202 / 1 = 2202 (the remainder is 0, so 1 and 2202 are divisors of 2202)
2202 / 2 = 1101 (the remainder is 0, so 2 and 1101 are divisors of 2202)
2202 / 3 = 734 (the remainder is 0, so 3 and 734 are divisors of 2202)
...
2202 / 45 = 48.933333333333 (the remainder is 42, so 45 is not a divisor of 2202)
2202 / 46 = 47.869565217391 (the remainder is 40, so 46 is not a divisor of 2202)